Sigurdsson also hit the post for the home side, who remain winless in the league since the opening day of the season, and find themselves second from bottom in the table.
"At the moment, it's just small margins," the 34-year-old told British media.
"Having said that, I think there is a lot to build on for the future and if we carry on performing like we did... (on Saturday), I am sure the results will come.
"We are certainly in a different situation than we are used to. And yes, it brings a different kind of pressure than we are used to. But as players you have to get on with it and stand up and be counted."
While Britton was aware that team spirit alone will not propel Swansea out of the relegation zone, he hoped the side could build on their encouraging performance against Watford.
"I know you need togetherness, spirit and camaraderie, but at the same time you need quality as well. You can't just rely on team spirit," Britton added.
"You need that quality and thankfully, I felt we showed that against Watford, so we need to make sure we carry on like that and keep improving our performances levels. If we do that, I am sure we will get the points we need."
Swansea next face Stoke City on Oct. 31.
(Reporting by Nivedita Shankar in Bengaluru, editing by Pritha Sarkar)
